Difference between revisions of "Manuals/calci/BETADISTX"

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*The beta distribution is a family of Continuous Probability Distributions defined on the interval [0, 1] parameterized by two positive shape parameters, denoted by <math>\alpha</math> and <math>\beta</math>.
 
*The beta distribution is a family of Continuous Probability Distributions defined on the interval [0, 1] parameterized by two positive shape parameters, denoted by <math>\alpha</math> and <math>\beta</math>.
 
*The Beta Distribution is also known as the Beta Distribution of the first kind.
 
*The Beta Distribution is also known as the Beta Distribution of the first kind.
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*In <math>BETADIST(x,\alpha,\beta)</math>, <math>x</math> is any real number.
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*In <math>BETADISTX(x,alpha,beta)</math>, <math>x</math> is any real number.
 
*alpha is the value of the shape parameter.
 
*alpha is the value of the shape parameter.
 
*beta is the value of the shape parameter
 
*beta is the value of the shape parameter
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<math>f(x)=\frac{x^{\alpha-1}(1-x)^{ \beta-1}}{B(\alpha,\beta)},</math> where <math>0 \le x \le 1</math>; <math>\alpha,\beta >0 </math> and <math>B(\alpha,\beta)</math> is the Beta function.
 
<math>f(x)=\frac{x^{\alpha-1}(1-x)^{ \beta-1}}{B(\alpha,\beta)},</math> where <math>0 \le x \le 1</math>; <math>\alpha,\beta >0 </math> and <math>B(\alpha,\beta)</math> is the Beta function.
 
*The formula for the Cumulative Beta Distribution is called the Incomplete Beta function ratio and it is denoted by <math>I_x</math> and is defined as :
 
*The formula for the Cumulative Beta Distribution is called the Incomplete Beta function ratio and it is denoted by <math>I_x</math> and is defined as :
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<math>F(x)=I_x(\alpha,\beta)=\int_{0}^{x}\frac{t^{α−1}(1−t)^{\beta−1}dt} {B(\alpha,\beta)}</math>,  where <math>0 \le x \le 1</math> ; <math>\alpha,\beta>0</math> and <math>B(\alpha,\beta)</math> is the Beta function.
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<math>F(x)=I_x(\alpha,\beta)</math>=<math>\int_{0}^{x}f(x)=\frac{t^{\alpha-1}(1-t)^{ \beta-1}dt}{B(\alpha,\beta)}</math>,  where <math>0 \le t \le 1</math> ; <math>\alpha,\beta>0</math> and <math>B(\alpha,\beta)</math> is the Beta function.
 
*This function will give the result as error when  
 
*This function will give the result as error when  
 
  1.Any one of the arguments are non-numeric.
 
  1.Any one of the arguments are non-numeric.
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  2.<math>\alpha \le 0</math> or <math>\beta \le 0</math>
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  2.<math>alpha \le 0</math> or <math>beta \le 0</math>
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==Examples==
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#=BETADISTX(0.67,9,12) = 0.3102416743686678
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#=BETADISTX(6,34,37) = 2.576888446568541e+72
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#=BETADISTX(100,456,467)= NaN
  
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==Examples==
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==Related Videos==
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#=BETADIST(0.4,8,10) = 0.35949234293309396
 
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#=BETADIST(3,5,9,2,6) = 0.20603810250759128
 
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#=BETADIST(9,4,2,8,11) = 0.04526748971193415
 
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#=BETADIST(5,-1,-2,4,7) = #ERROR
 
  
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{{#ev:youtube|aZjUTx-E0Pk|280|center|Beta Distribution}}
  
 
==See Also==
 
==See Also==
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==References==
 
==References==
 
[http://en.wikipedia.org/wiki/Beta_distribution  Beta Distribution]
 
[http://en.wikipedia.org/wiki/Beta_distribution  Beta Distribution]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 15:01, 4 December 2018

BETADISTX(x,alpha,beta)


  • is any real number.
  • alpha and beta are the value of the shape parameter

Description

  • This function gives the Cumulative Beta Probability Density function.
  • The beta distribution is a family of Continuous Probability Distributions defined on the interval [0, 1] parameterized by two positive shape parameters, denoted by and .
  • The Beta Distribution is also known as the Beta Distribution of the first kind.
  • In , is any real number.
  • alpha is the value of the shape parameter.
  • beta is the value of the shape parameter
  • The Probability Density Function of the beta distribution is:

where ; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha,\beta >0 } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(\alpha,\beta)} is the Beta function.

  • The formula for the Cumulative Beta Distribution is called the Incomplete Beta function ratio and it is denoted by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I_x} and is defined as :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(x)=I_x(\alpha,\beta)} =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{x}f(x)=\frac{t^{\alpha-1}(1-t)^{ \beta-1}dt}{B(\alpha,\beta)}} , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 \le t \le 1} ; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha,\beta>0} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(\alpha,\beta)} is the Beta function.

  • This function will give the result as error when
1.Any one of the arguments are non-numeric.
2.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle alpha \le 0}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle beta \le 0}

Examples

  1. =BETADISTX(0.67,9,12) = 0.3102416743686678
  2. =BETADISTX(6,34,37) = 2.576888446568541e+72
  3. =BETADISTX(100,456,467)= NaN

Related Videos

Beta Distribution

See Also

References

Beta Distribution


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